From the point she fell asleep, she slept twice as long as the rest of the flight after waking. Does that smell like 2/3 + 1/3 to you?

Back to the halfway bit...

She slept 2/3 of the second half of the flight.

She slept 2/3 of half of the flight.

She slept 2/3 * 1/2 of the flight.

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